Secure data processing

ABSTRACT

A first system creates and sends encryption key data to multiple data sources. A second system receives data encrypted using the encryption key data from the multiple data sources; the data may include noise data such that, even if decrypted, the original data cannot be discovered. Because the encryption is additively homomorphic, the second system may create encrypted summation data using the encrypted data. The first system separately receives the noise data encrypted using the same technique as the encrypted data. The second system may send the encrypted summation data to the first system, which may then remove the noise data from the encrypted summation data to create unencrypted summation data.

CROSS-REFERENCE TO RELATED APPLICATION DATA

This application claims the benefit of and priority to U.S. Provisional Patent Application No. 62/646,525, filed Mar. 22, 2018, and entitled “A SECURE SYSTEM FOR DISTRIBUTED DATA ANALYSIS,” in the names of Jeremy Taylor, et al. The above provisional application is herein incorporated by reference in its entirety.

BACKGROUND

Data security and encryption is a branch of computer science that relates to protecting information from disclosure to third parties and allowing only an intended party or parties access to that information. The data may be encrypted using various techniques, such as public/private key cryptography, and may be decrypted by the intended recipient using a shared public key and a private key. Transmission of the data is protected from being decrypted by third parties at least by their lack of possession of the private key.

BRIEF DESCRIPTION OF DRAWINGS

For a more complete understanding of the present disclosure, reference is now made to the following description taken in conjunction with the accompanying drawings.

FIGS. 1A and 1B illustrate systems configured to securely process data according to embodiments of the present disclosure.

FIG. 1C illustrates a system configured to securely train a neural-network model according to embodiments of the present disclosure.

FIG. 1D illustrates a system configured to conduct transactions related to securely training a neural-network model according to embodiments of the present disclosure.

FIGS. 2A and 2B illustrate computing environments including a secure data processor according to embodiments of the present disclosure.

FIGS. 3A-3H illustrate data transfers using computing environments that include a secure data processor according to embodiments of the present disclosure.

FIGS. 4A and 4B illustrate components for training a neural network according to embodiments of the present disclosure.

FIGS. 5A and 5B illustrate a flow diagram for transacting to build a neural network according to embodiments of the present disclosure.

FIG. 6 illustrates an example structure of a neural network according to embodiments of the present disclosure.

FIG. 7 illustrates an example structure of a recurrent neural network according to embodiments of the present disclosure.

FIG. 8 illustrates a long-short-term memory (LSTM) cell according to embodiments of the present disclosure.

FIG. 9 is a conceptual diagram of components of a system according to embodiments of the present disclosure.

FIG. 10 is a conceptual diagram of a network according to embodiments of the present disclosure.

SUMMARY

In various embodiments of the present disclosure, a first party that owns proprietary data permits a second party to realize a benefit from the data without actually having to transfer the data; the first party shares only an encrypted version of the data. In some embodiments, a secure data processor is disposed between the first and second parties on a computer network; two or more data sources send encrypted versions of their data to the secure data processor, which adds them together and sends the result to the second party. The secure data processor cannot decrypt the data because it lacks the necessary keys, and the second party can decrypt only the sum of the data, not the original data.

In some embodiments, multiple data sources encrypt data using encryption key data received from a first system; a second system does not have access to the encryption key data. The second system receives the encrypted data from the multiple data sources. Because the encryption is additively homomorphic, the second system may create encrypted summation data using the encrypted data. The second system may send the encrypted summation data to the first system, which may then decrypt the encrypted summation data to create unencrypted summation data.

In other embodiments, the data source may include noise with the data. A first system creates and sends encryption key data to multiple data sources. A second system receives data encrypted using the encryption key data from the multiple data sources; the data may include noise data such that, even if decrypted, the original data cannot be discovered. Because the encryption is additively homomorphic, the second system may create encrypted summation data using the encrypted data. The first system separately receives the noise data encrypted using the same technique as the encrypted data. The second system may send the encrypted summation data to the first system, which may then remove the noise data from the encrypted summation data to create unencrypted summation data.

In other embodiments, a neural-network model may be securely trained. Computer instructions corresponding to a neural-network model are received and encrypted using an encryption technique. The model is trained using the training data using, for example, a gradient descent technique, and gradient data encrypted using the encryption technique is received from a data source. If the model performs in accordance with a quality metric, it is sent to a device of a model user.

In still other embodiments, a marketplace may be configured to request building the model and to offer to build the model. A request to train a neural-network model is received, as are a first offer to supply encrypted training data and a second offer to train the model. After determining that the offers satisfy the request, a model provider told to train the model. If they model performs in accordance with a quality metric, it is sent to a model user

DETAILED DESCRIPTION

Machine-learning systems, such as those that use neural networks, may be trained using training data and then used to make predictions on out-of-sample (i.e., non-training) data. A power company, for example, may collect data regarding a failure likelihood of a particular component; this data may include, for example, temperature, vibration, and voltage data collected during use of the component. The power company may then annotate this data to indicate times at which the component failed. Using this collected and annotated data, the power company may train a neural network to predict when the component will fail based on the already-known times of failure. Once built, the power company may deploy the model to attempt to receive additional data collected from the component and make failure predictions for currently operating components using this out-of-sample data.

The training data may, however, be insufficient in size and/or quality to train a model that predicts component failures with an acceptable accuracy. The power company may improve their model by training it with additional training data, but this additional training data may not be accessible to the power company. A rival power company, for example, may possess some additional training data, but may be reluctant to provide their proprietary intellectual property to a competitor. In other industries or situations, data owners may further be predisposed to not share their data because the data set is too large to manage or because it is in a different format from other data. In still other industries, data owners may be prohibited to share data, such as medical data, due to state laws and/or regulations. A data owner may further be predisposed to not share data, especially publicly, because any further monetary value in the sharing of the data is lost after sharing the data once.

Embodiments of the present disclosure thus relate to systems and methods for securely processing data, such as the training data described above, collected from one or more data sources. The data sources encrypt their data in accordance with the methods described herein; the data sources may add noise to their data to further protect it. The data sources may send their encrypted, noisy data to a secure data processor, which may add each bit of encrypted, noisy data together to create a sum. Either the secure data processor itself, or another system designed to create a model, receives encrypted noise from the data sources. Using the sum of the encrypted, noisy data and the encrypted noisy data, the secure data processor and/or other system removes the noise to create a sum of the data; this sum may be used to train a model that may be of benefit to the one or more data sources (and/or other users of the model). In some embodiments, the data sources encrypt their data in accordance with a set of domain parameters corresponding to an encryption technique, such as Rivest-Shamir-Adleman (RSA) encryption, Advanced Encryption Standard (AES) encryption, or elliptic-curve encryption; in these embodiments, the data source may send only their encrypted data and may not send the encrypted noise data. A marketplace may be configured to facilitate transactions between the data sources and other systems. The data sources thus may benefit financially, or by use of the trained model, without divulging their training data to any other party.

FIGS. 1A-1D show systems that include a secure data processor 120 and a network 199. The network 199 may include the Internet and/or any other wide- or local-area network, and may include wired, wireless, and/or cellular network hardware. The secure data processor 120 may communicate, via the network 199, with one or more model providers 122, model users 124, and/or data sources 126. The secure data processor 120 may transmit, via the network 199, requests to the other systems using one or more application programming interfaces (APIs). Each API may correspond to a particular application. A particular application may, for example, be operated within the secure data processor 120 or may be operating using one or more of the other systems.

Referring first to FIG. 1A, in accordance with the present disclosure, a system 100 a includes a secure data processor 120 a, a model provider 122 a, a model user 124, and one or more data sources 126. The model provider 122 a sends (130), to a first data source, encryption key data. The model provider 122 a also sends (132) to a second data source, the encryption key data. The secure data processor 120 a receives (134), from the first data source, first encrypted input data, the first encrypted input data being encrypted based at least in part on the encryption key data. The secure data processor 120 a receives (136), from the first data source, second encrypted input data, the second encrypted input data being encrypted based at least in part on the encryption key data. The secure data processor 120 a generates (138), encrypted summation data corresponding to a sum of the first encrypted input data and the second encrypted input data, wherein the secure data processor 120 is not in possession of the encryption key data. The secure data processor 120 a sends (140), to the other of the model provider 122 a, using a secure connection, the encrypted summation data. The model provider 122 a generates (142) summation data by decrypting, based at least in part on the encryption key data, the encrypted sum data

Referring to FIG. 1B, in accordance with the present disclosure, a system 100 b includes a secure data processor 120, a model provider 122, a model user 124, and one or more data sources 126. The secure data processor 120 b and/or model provider 122 b receives (144), from a first data source, first encrypted input data. The secure data processor 120 b and/or model provider 122 b receives (146), from the first data source, first encrypted noise data. The secure data processor 120 b and/or model provider 122 b receives (148), from a second data source, second encrypted input data. The secure data processor 120 b and/or model provider 122 b receives (150), from the second data source, second encrypted noise data. The secure data processor 120 b and/or model provider 122 b generates (152) encrypted summation data corresponding to a sum of the first encrypted input data and the second encrypted input data. The secure data processor 120 b and/or model provider 122 b generates (154) summation data by decrypting, based at least in part on the first encrypted noise data and the second encrypted noise data, the encrypted sum data.

Referring to FIG. 1C, in accordance with the present disclosure, a system 100 c includes a secure data processor 120 c, a model provider 122 c, a model user 124, and one or more data sources 126. The secure data processor 120 c (and/or other system) receives (156), from a model provider, computer instructions corresponding to a neural-network model. The secure data processor 120 c determines (158) encrypted computer instructions by encrypting, using an encryption technique, at least a portion of the computer instructions. The secure data processor 120 c receives (160), from a first data source, first encrypted change data corresponding to weights of the model, the first encrypted change data being encrypted using the encryption technique. The secure data processor 120 c receives (162), from a second data source, second encrypted change data, the second encrypted change data being encrypted using the encryption technique. The secure data processor 120 c determines (164) an encrypted summation change data by summing the first encrypted changes data and the second encrypted change data. The secure data processor 120 c determines (166) that a metric associated with the changes satisfies a threshold and determines (168) decrypted change data.

Referring to FIG. 1D, in accordance with the present disclosure, a system 100 d includes a secure data processor 120, a model provider 122, a model user 124, and one or more data sources 126. The secure data processor 120 d (and/or other system) receives (170), from a model user, a first request to provide a trained neural-network model. The secure data processor 120 d receives (172), from a data source, a first offer to provide first encrypted input data. The secure data processor 120 d receives (174), from a model provider 122 d, a second offer to train a first neural-network model. The secure data processor 120 d determines (176) that the first offer and the second offer satisfy the first request. The secure data processor 120 d sends (178), to the model provider 122 d, a second request to train a second neural-network model using the first neural-network model and the first encrypted training data. The secure data processor 120 d receives (180), from the model provider 122 d, the second neural-network model. The secure data processor 120 d determines (182) that the second neural-network model satisfies a quality metric and, based thereon, sends (184), to the model user 124, the second neural-network model.

FIGS. 2A and 2B illustrate computing environments including a secure data processor 120 according to embodiments of the present disclosure. A secure data processor 120, described in greater detail below, may be one or more servers configured to receive encrypted data from one or more data sources 126. A model provider 122 may provide and/or train a model, such as a neural-network machine-learning model, configured to process the data from the data sources 126. The secure data processor 120 and/or the model provider 122 may train the model using the data from the data sources 126 by, for example, computing weights of the machine-learning model using, for example, stochastic gradient descent. Once the secure data processor 120 and/or model provider 122 trains the model the model in accordance with one or more metrics, it may send the trained model and/or associated weights to one or more model users 124. In some embodiments, a model user 124 is also a data source 126.

Although the secure data processor 120, the model provider 122, model user 124, and data sources 126 are illustrated as separate systems, in some embodiments, one or more of the secure data processor 120, the model provider 122, model user 124, and data sources 126 may be the same system. For example, the model provider 122 may also be the model user 124. One or more of the data sources 126 may be the model user 124. The present disclosure is thus not limited to the example environment illustrated in FIG. 2A.

FIG. 2B illustrates a computing environment that includes a blockchain database 202. The blockchain database 202 may use blockchain technology, as one of skill in the art will understand, to maintain a public ledger of information, such as data transmitted using the secure data processor 120. The secure data processor may not communicate directly with the blockchain database 202; instead, it may communicate using a blockchain market 204 and/or a blockchain agent 206.

The blockchain market 204 may include pointers to data in one or more data sources 126 and may allow access to that data. The blockchain market 204 may further contain information related to one more self-performing contracts (i.e., “smart” contracts) relating to data processes or transmitted by the secure data processor 120. The blockchain agent 206, which may be referred to as an “oracle,” may monitor the blockchain database 202 for information and/or changes to information therein, and may transmit data relating to those changes to the secure data processor 120.

FIGS. 3A-3F illustrate data transfers using computing environments that include a secure data processor 120 according to embodiments of the present disclosure. Referring first to FIG. 3A, the model provider 122 sends a model 302 to the secure data processor 120. The model 302 may be, as explained herein, a neural-network model. The secure data processor 120 may send the model 302 to one or more data sources 126 and, once the model is trained, to the model user 124.

In FIGS. 3A and 3B, in various embodiments, the model provider 122 creates and transmits encryption key data including at least one or more keys 304. The creator of the encryption key data may correspond to an entity trusted to learn the sum of, but not the individual values of, data owned by data sources 126. In some embodiments, as described in further detail below, the secure data processor 120 is trusted to learn only the encrypted sum of the data owned by the data sources 126 and is not trusted to learn the unencrypted sum of the data. The secure data processor 120 may then send this encrypted sum to the model provider 122, which may determine the unencrypted sum. In these embodiments, as shown in FIG. 3B, the model provider 122 creates and distributes the encryption key data.

The encryption key data may include a modulus n, an exponent e, and/or an element a (as explained in greater detail below). The model provider 122 may determine the modulus n by multiplying two prime numbers p and q. The prime numbers may, in some embodiments, be Sophie Germain prime numbers and may be, for example, approximately 1024 bits in size, and the modulus n may be approximately 2048 bits in size. The prime numbers p and q may be defined using the below equations (1) and (2).

p=2p′+1  (1)

q=2q′+1  (2)

The numbers p′ and q′ may also be prime numbers. The model provider 122 may further compute the public modulus n in accordance with the below equation (3). The public modulus n may, as explained in greater detail below, be sent to and used by a data source 126.

n=pq  (3)

The model provider 122 may further compute a function used to select the exponent e that may further be sent to and used by a data source 126. In some embodiments, this function is a Carmichael's totient function λ(n), which may be determined in accordance with the below equation (4), in which lcm(x, y) finds the least common multiple of x and y.

λ(n)=lcm(p−1,q−1)  (4)

Using equations (1) and (2), equation (4) may be expressed as the below equation (5).

λ(n)=2p′q′  (5)

The value of λ(n) may be at least 2046 bits in size. The public exponent e may then be determined using the below equation (6), in which gcd(x,y) finds the greatest common denominator of x and y.

gcd(λ(n),e)=1  (6)

The model provider 122 may further determine the modular multiplicative inverse d of e in accordance with the below equation (7), in which mod x computes the modulus of x.

d=e ⁻¹ mod λ(n)  (7)

The model provider 122 may then select an element a of maximum order in a multiplicative group Z_(n)*, wherein the maximum order of the multiplicative group Z_(n)* is 2p′q′, in accordance with known methods of finding an element of maximum order. In some embodiments, the model provider 122 finds a first generator g₁ of Z_(p)* in which n=p−1, finds a second generator g₂ of Z_(q)* in which n=q−1, and then uses Gauss's Algorithm to find the element a such that a=g₁ (mod p) and a=g₂ (mod q) and such that 1≤a≤n−1. The generators may be found by choosing a random element of the multiplicative group Z_(n)*, computing b in accordance with the below equation (8), and determining if b is equal to one. If b is equal to one, another random element is chosen and b is again computed. If b is not equal to one, b is selected as the element a.

b←α ^(n/p) ^(i)   (8)

Gauss's Algorithm may be used to find a in accordance with the below equations (9), (10), and (11).

a=Σ _(i=1) ^(k) a _(i) N _(i) M _(i) mod(n)  (9)

In the above equation (9), N_(i) may be determined in accordance with the below equation (10).

$\begin{matrix} {N_{i} = \frac{n}{n_{i}}} & (10) \end{matrix}$

M_(i) may be determined in accordance with the below equation (11).

M _(i) =N _(i) ⁻¹ mod(n _(i))  (11)

The model provider 122 may further send the element a to the data sources 126, which may further use the element a to encrypt data as explained in greater detail below. The model provider 122 may, however, keep the multiplicative inverse d secret.

The data sources 126 may encrypt data in accordance with an encryption function H(m). In some embodiments, the encryption function H(m) is defined using the below equation (12), in which m is less than the value of the Carmichael's totient function λ(n).

H(m)=a ^(me)(mod n)  (12)

The model provider 122 may decrypt data in accordance with a decryption function H⁻¹(c). In some embodiments, the decryption function H⁻¹(c) is defined using the below equation (13), in which log_(a) is the discrete logarithm function over base a. The algorithm function log, may be computed by using, for example, a “baby-step giant-step” algorithm.

H ⁻¹(c)=log_(a)(c ^(d))(mod n)  (13)

In various embodiments, data encrypted using the encryption function H(m) is additively homomorphic such that H(m₁+m₂) may be determined in accordance with the below equations (14) and (15).

H(m ₁ +m ₂)=a ^((m) ¹ ^(+m) ² ^()e)(mod n)  (14)

H(m ₁ +m ₂)=a ^(m) ¹ ^(e) a ^(m) ² ^(e)(mod n)  (15)

In some embodiments, the above equations (14) and (15) may be computed or approximated by multiplying H(m1) and H(m2) in accordance with the below equation (16).

H(m ₁ +m ₂)=H(m ₁)H(m ₂)  (16)

The secure data processor 120 may thus, given two items of encrypted data H(m₁) and H(m₂), determine H(m₁+m₂) without first applying the decryption function H⁻¹(c). In some embodiments, the value of m is 32 bits in size.

Referring to FIG. 3C, the data sources 126 may encrypt data plus noise (ν_(i)+η_(i)) in accordance with a first encryption function H(m), as described above, and may encrypt noise (η_(i)) in accordance with a second encryption function K(m). In some embodiments, the model provider 122 creates the second encryption function K(m) using the above-described process of creating the first encryption function H(m). The second encryption function K(m) may, however, use a different set of keys, including but not limited to a different public key, which it may receive from the model provider 122. The data source 126 may encrypt (ν_(i)+η_(i)) using one encryption function (for example, H(m)) and may encrypt (η_(i)) using a different encryption function (for example, K(m)). A data source 126 may determine a value ν_(i) that it wishes to make available for training of the model 302 without allowing knowledge of the actual value of ν_(i) to be possessed by the secure data processor 120, model provider 122, and/or model user 124. The value ν_(i) may be 32 bits in size.

The data source 126 selects the random noise value using, for example, a random noise generator. The noise value η_(i) may be 368 bits in size. Using the above encryption function H(m), each data source 126 computes H(ν_(i)+η_(i)) 310 and each data source 126 computes K(η_(i)) 312 using the second encryption function K(m). Each data source 126 may then send H(ν_(i)+η_(i)) 310 and K(η_(i)) 312 to the secure data processor 120. The data source 126 may thereafter delete the noise value η_(i) to thereby prevent its re-use with subsequent encryption.

The secure data processor 120 may determine that it has received the encrypted data plus noise 310 and the encrypted noise 312 from the data sources 126. Once the encrypted data plus noise 310 and the encrypted noise 312 is received, the secure data processor 120 computes the sum H(Σν_(i)+Ση_(i)) 316 of the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n and the sum K(Ση_(i)) 318 of the encrypted noise data K(η_(i)) 312 a, 312 b, . . . 312 n. As explained above, because the encryption functions H(m) and K(m) are additively homomorphic, the sum H(Σν_(i)+Ση_(i)) 316 of the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n and the sum K(Ση_(i)) 318 of the encrypted noise data K(η_(i)) 312 a, 312 b, . . . 312 n may be determined by multiplying and/or modulo-multiplying each encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n and encrypted noise data K(η_(i)) 312 a, 312 b, . . . 312 n in accordance with one or more of equations (14), (15), and/or (16). The secure data processor 120 may then send the sum H(Σν_(i)+Ση_(i)) 316 and the sum K(Ση_(i)) 318 to the model provider 122.

The model provider 122 may decrypt the sum H(Σν_(i)+Ση_(i)) 316 using the decryption function H⁻¹(c) and may decrypt the sum K(Ση_(i)) 318 using the decryption function K⁻¹(c). The model provider 122 may then subtract the sum of the decrypted noise data Ση_(i) from the sum of the values-plus-noise data Σ(ν_(i)+η_(i)) to determine the sum Σν_(i) 314 of the values ν_(i).

Referring to FIG. 3D, in some embodiments, the secure data processor 120 may include a first secure data processor 120 x and a second secure data processor 120 y. The first secure data processor 120 x and second secure data processor 120 y may be untrusted entities and may thus not be trusted to discover the value of the summed data Σν_(i). The first secure data processor 120 x may receive the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, 310 n and send the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n to the model provider 122. The second secure data processor 120 y may receive the encrypted noise data H(η_(i)) 312 a, 312 b, . . . 312 n and may compute the sum H(Ση_(i)) 314 of the encrypted noise data H(η_(i)) 312 a, 312 b, . . . 312 n, and may send the sum H(Ση_(i)) 314 to the model provider 122. The model provider 122 may then remove the sum H(Ση_(i)) 314 from the sum H(Σν_(i)+Ση_(i)) 316 to determine the sum Σν_(i) of the values ν_(i), as described above.

Referring to FIG. 3E, and with reference also to FIG. 3C, in some embodiments, the secure data processor 120 may include a first secure data processor 120 x and a second secure data processor 120 y. As discussed above with reference to FIG. 3C, each data source may encrypt the values-plus noise data ν_(i)+η_(i) with a first encryption function H(m) to create the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n, and may encrypt the noise data with a second encryption function K(m) to create the encrypted noise data K(η_(i)) 312 a, 312 b, . . . 312 n. A first secure data processor 120 x may sum the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n to create the sum H(Σν_(i)+Ση_(i)) 316, and a second secure data processor 120 y may sum the encrypted noise data K(η_(i)) 312 a, 312 b, . . . 312 n to create the sum H(Ση_(i)) 314. The model provider 122, as described above, may then remove the sum K(Ση_(i)) 314 from the sum H(Σν_(i)+Ση_(i)) 316 to determine the sum Σν_(i) of the values ν_(i).

Referring to FIG. 3F, in some embodiments, the data sources 126 send the encrypted noise data H(η_(i)) 312 to the model provider 122 because the secure data processor 120 is not trusted to learn the sum Σν_(i) 314 of the data ν_(i). In these embodiments, the data sources 126 compute the values-plus-noise data H(ν_(i)+η_(i)) 310, as described above, and send the values-plus-noise data H(ν_(i)+η_(i)) 310 to the secure data processor 120. The data sources 126 similarly compute the noise data H(η_(i)) 312, as described above, but send the noise data H(η_(i)) 312 to the model provider 122, not the secure data processor 120. The secure data processor 120 computes the sum H(Σν_(i)+Ση_(i)) of the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n. As explained above, because the encryption function H(m) is additively homomorphic, the sum H(Σν_(i)+Ση_(i)) of the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n may be determined by multiplying each encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n.

The secure data processor 120 may then send the sum H(Σν_(i)+Ση_(i)) 316 of the encrypted values-plus-noise data H(ν_(i)+η_(i)) 310 a, 310 b, . . . 310 n to the model provider 122. The model provider 122 may then remove the encrypted noise data H(η_(i)) 312 a, 312 b, . . . 312 n from the sum H(Σν_(i)+Ση_(i)) 316 to determine the encrypted sum H(Σν_(i)) and, finally, the sum Σν_(i) 314. In some embodiments, the model provider 122 may decrypt each encrypted noise data H(η_(i)) 312 a, 312 b, . . . 312 n using the decryption function H⁻¹(c). The model provider 122 may then decrypt the sum of the encrypted values-plus-noise data H(ν_(i)+η_(i)) and subtract the decrypted noise data from the sum of the decrypted values-plus-noise data (ν_(i)+η_(i)) to determine the sum (Σν_(i)) of the values ν_(i). In other embodiments, the model provider 122 subtracts the encrypted noise data H(η_(i)) 312 a, 312 b, . . . 312 n from the sum H(Σν_(i)+Ση_(i)) 316 to determine the encrypted sum H(Σν_(i)) 314. The model provider 122 may subtract the encrypted noise data H(η_(i)) 312 a, 312 b, . . . 312 n individually or may, in some embodiments, add the encrypted noise data H(η_(i)) 312 a, 312 b, . . . 312 n together to create summed encrypted noise data H(Ση_(i)) before subtracting it from the encrypted sum H(Σν_(i)+Ση_(i)) 316. The model provider 122 may then determine the sum Σν_(i) 314 of the data ν_(i) using the decryption function H⁻¹(c).

FIG. 3G illustrates a system for secure data processing in accordance with the present disclosure. In various embodiments, the system of FIG. 3G permits processing of integers and fixed-point numbers having sizes greater than 32 bits and permits up to 2 m data sources 126, where m is between 2 and 31 and wherein a block size is as large as 32-m. The value m may be, in some embodiments, 16. In various embodiments, a given fixed-point number f_(i) may be expressed as an integer u_(i) in accordance with the below equation (17).

$\begin{matrix} {f_{i} = \frac{u_{i}}{10^{s}}} & (17) \end{matrix}$

In equation (15), s is any integer; the equation thus shifts the decimal point of f_(i) to the right or left some number of places. In some embodiments, the decimal point is shifted to the right a number of places necessary to convert the fixed-point f_(i) to the integer u_(i). The secure data processor 120, model provider 122, and data sources 126 may all use the same value for s. If s is smaller than the actual number of decimal places of f_(i), the integer u_(i) may represent a rounded value of f_(i); if s is larger than the actual number of decimal places of f_(i), the integer u_(i) may include a number of zeros at its end. The sum of the f_(i) values may similarly relate to the sum of the u_(i) values in accordance with the below equation (18).

$\begin{matrix} {{\Sigma \; f_{i}} = \frac{\Sigma \; u_{i}}{10^{s}}} & (18) \end{matrix}$

Each integer value u_(i) may be expressed as a sum of 16-bit blocks in accordance with the below equation (19).

$\begin{matrix} {u_{i} = {\sum\limits_{i}{\sum\limits_{j}\frac{u_{ij}}{2^{16j}}}}} & (19) \end{matrix}$

Thus, u_(i) may be defined as a set of values <u_(ij)>, where u_(ij) is the value for each 16-bit block. Each value of u_(ij) may be between −2¹⁵ and 2¹⁵−1; because each block is 16 bits, the sum of all the values of u_(ij) may between −2³¹ and 2³¹−1. In addition, because each block is 16 bits, there may be up to 2¹⁶ data sources 126.

Thus the model provider 122 may define the value s and transmit the value s to the data sources 126. The model provider 122 may similarly define and transmit a block size, such as 16 bits, to the secure data processor 120, data sources 126, and/or model user 124. Each data source 126 possesses at least one fixed-point value f_(i), which it converts to the corresponding integer u_(i) in accordance with equation (19), and may compute u_(i)=<u_(ij)> using the value s and the block size, in accordance with equation (16). The data sources 126 may encrypt these values using the encryption function H(m), as described above, and send the encrypted data to the secure data processor 120. The secure data processor 120 may compute the sum of all the encrypted data received from the data sources 126, as described above, and send the sum to the model provider 122. The model provider 122 may compute the unencrypted sum of all the encrypted data using the decryption function H⁻¹(c), as described above, and may convert the integer value u_(i) to its corresponding fixed-point value f_(i) using equation (19).

The data sources 126 may determine and use a noise value noise value η_(i) when sending the data to the secure data processor 120, as described above. In some embodiments, in addition to using the noise value η_(i) as described above, the data sources determine and use a second noise value p_(i). For example, in cases in which u_(i) is small and j is large, some values of u_(ij) may be zero. If u_(ij) is zero, the encrypted value H(u_(ij)+η_(i)) becomes simply H(η_(i)), and a component of the system not permitted to learn η_(i), such as, in some embodiments, the secure data processor 120, could learn noise value η_(i) simply by decrypting H⁻¹(u_(ij)+η_(i)).

Thus, in some embodiments, the data source 126 adds the second noise value p_(i) to the integer value u_(i) before processing the integer value u_(i). The data sources 126 send the encrypted data plus first noise value 320 to the secure data processor 120; the data sources 126 also send the encrypted first noise value and the encrypted second noise value 322 to the model provider 122. After computing u_(i) as described above, the model provider 122 may decrypt the encrypted second noise value p_(i) and remove it from the data value u_(i), as described above.

Referring to FIG. 3H, in some embodiments, the secure data processor 120, model user 124, and/or data sources 126 may use elliptic-curve cryptography to securely process, send, and/or receive data. Elliptic-curve cryptography utilizes an elliptic curve to encrypt data, as opposed to multiplying two prime numbers to create a modulus, as described above. An elliptic curve E is a plane curve over a finite field F_(p) of prime numbers that satisfies the below equation (20).

y ² =x ³ +ax+b  (20)

The finite field F_(p) of prime numbers may be, for example, the NIST P-521 field defined by the U.S. National Institute of Standards and Technology (NIST). In some embodiments, elliptic curves over binary fields, such as NIST curve B-571, may be used as the finite field F_(p) of prime numbers. A key is represented as (x,y) coordinates of a point on the curve; an operator may be defined such that using the operator on two (x,y) coordinates on the curve yields a third (x,y) coordinate also on the curve. Thus, key transfer may be performed by transmitting only one coordinate and identifying information of the second coordinate.

The above elliptic curve may have a generator point, G, that is a point on the curve—e.g., G=(x,y)∈E. A number n of points on the curve may have the same order as G—e.g., n=o(G). The identity element of the curve E may be infinity. A cofactor h of the curve E may be defined by the following equation (21).

$\begin{matrix} {h = \frac{{E\left( F_{p} \right)}}{o(G)}} & (21) \end{matrix}$

A first party, such as the model provider 122, may select a private key n_(B) that is less than o(G). In various embodiments, the secure data processor 120 is not the first party and thus does not know the private key n_(B). The first party may generate a public key P_(B) in accordance with equation (22).

P _(B) =n _(B) G=Σ _(i) ^(n) ^(B) G  (22)

The first party may then transmit the public key P_(B) to a second party, such as a data source 126. The first party may similarly transmit encryption key data corresponding to domain parameters (p, a, b, G, n, h). The data source 126 may then encrypt data m using the public key P_(B). The data source 126 may first encode the data m; if m is greater than zero, the data source 126 may encode it in accordance with mG; m is less than zero, the data source 126 may encode it in accordance with (−m)G⁻¹. If G=(x,y), G⁻¹=(x,−y). In the below equations, however, the encoded data is represented as mG for clarity. The data source 126 may perform the encoding using, for example, a doubling-and-adding method, in O(log(m)) time.

To encrypt the encoded data mG, the data source 126 may select a random number c, wherein c is greater than zero and less than a finite field prime number p. The data source 126 may thereafter determine and send encrypted data in accordance with the below equation (23).

{cG,mG+CP _(B)}  (23)

The model provider 122 may receive the encrypted data from the data source 126 and may first determine a product of the random number c and the public key P_(B) in accordance with equation (24).

cP _(B) =c(n _(B) G)=n _(B)(cG)  (24)

The model provider 122 may then determine a product of the data m and the generator point Gin accordance with the below equation (25).

mG=(mG+cP _(B))−n _(B)(cG)  (25)

Finally, the model provider 122 may decode mG to determine the data m. This decoding, which may be referred to as solving the elliptic curve discrete logarithm, may be performed using, for example, a baby-step-giant-step algorithm in O(√{square root over (m)}) time.

As shown in FIG. 3H, each data source 126 encrypts data ν_(i) using the public key P_(B) and a selected random value c to create encrypted data 330 in accordance with the above equation (23). The data ν_(i) may be a 32-bit signed integer value. The encrypted data 330 may correspond to a pair of integers; the first integer may be (c_(i)G), and the second integer may be (ν_(i)G+c_(i)P_(B)). Each data source 126 may then send the encrypted data 330 to the secure data processor 120 using, in some embodiments, a secure connection. Because, as described above, the encrypted data 330 is additively homomorphic, the secure data processor 120 may compute the sum 332 of the received data 330 in accordance with the above equations (14), (15), and/or (16). The secure data processor 120 may then send the sum 332 to the model provider 122. The sum 332 may correspond to a pair of integers; the first integer may be Σ(c_(i)G), and the second integer may be (Σν_(i)G+Σc_(i)P_(B)).

The model provider 122 may decrypt the sum 332 by first determining the product of the sum of the random numbers c and the public key P_(B) (i.e., the second half of the second integer of the sum 332), using the first integer, the private key n_(B), and the generator G, in accordance with the below equation (26).

Σ_(i) c _(i) P _(B)=Σ_(i) c _(i)(n _(B) G)=n _(B)(Σ_(i) c _(i) G)  (26)

The model provider 122 may then determine the product of the sum of the data ν_(i) and G by subtracting the second half of the second integer of the sum 332 from the second integer of the sum 332 in accordance with the below equation (27).

Σ_(i)ν_(i) G=(Σ_(i)ν_(i) G+Σ _(i) c _(i) P _(B))−Σ_(i) c _(i) P _(B)  (27)

The model provider 122 may then decode the sum Σν_(i)G to determine Σv_(i) using, as described above, a baby-step-giant-step algorithm.

In some embodiments, with reference also to FIG. 3H and associated text, the secure data processor 120, model provider 122, model user 124, and/or data sources 126 send and receive data in blocks, such as 16-bit blocks, which permits the sending and receiving of fixed point numbers and/or integers larger than 32 bits. The model provider 122 may determine an integer s in accordance with equation 17 and transmit the integer s to the data sources 126. Each data source 126 may then convert a fixed point number to an integer in accordance with equation (18) and/or create a number 16-bit blocks representing the number in accordance with equation (19) prior to sending encrypting and sending the data 330.

FIGS. 4A and 4B illustrate a secure data processor 120 for training a neural network according to embodiments of the present disclosure. A code encryption component 402 receives, from a model provider 222, unencrypted code describing a model, such as a neural network. The model may include configurable values that control the output of the model given inputs to the model; these configurable values are referred to herein as weights (as described in greater detail with reference to FIG. 8). The code encryption component 402 encrypts the code (which may include encrypting the model and/or weights associated with the model) using, for example, the encryption function H(m) described herein. The encryption function H(m), and its associated public and private encryption key data described herein, may be created by the model provider 122, and the public encryption key data may be sent to the data sources 126. In some embodiments, the encryption function H(m) and its associated public and private encryption key data is created by the model owner 124. In these embodiments, the model owner 124 may use the encryption key data to decrypt a trained neural network, while the model provider 122 is prevented from decrypting the trained neural network. In these embodiments, the model owner 124 may additionally decrypt training data during training of the model, such as the performance metrics described herein.

A send/receive component 404 receives the encrypted computer instructions from the code encryption component 402, which it may send to the data sources 126. The send/receive component 404 further receives a set of initial weights from an initial-weight generation component 406. The initial weights may be random values; the initial-weight generation component 406 may include, for example, a random-number generator and may generate fixed-point random numbers between 0.0 and 1.0 as the initial weights. Because the initial weights are random, if a third party were to possess only the weight updates, as described below, the third party would not be able to derive the actual weights at least because possession of both the weight updates and the initial weights is necessary to derive the actual weights.

The send/receive component 404 receives, from one or more data sources 126, change data encrypted using the techniques described herein, such as by using the encryption function H(m). The encrypted change data may include changes in weights (i.e., weight updates) corresponding to a model, gradients corresponding to a model, and/or metrics of performance of the model as modified with the changes and/or gradients. Each data source 126 may create model-output data by applying, to a copy of the model, the values ν_(i) described herein using a secure data processor 128, which may be a gradient-descent processor. Using the gradient descent techniques described herein, the secure data processor 128 applies the values ν_(i) to the model and determines, based on outputs of the model, one or more weight updates and/or one or metrics of accuracy of the outputs of the model.

The metrics may include, for example, a degree of similarity between outputs of the model and outputs expected from training data. A metric of 100 may, for example, indicate perfect similarity, while a metric of 0 may indicate no similarity. Based on the performance of the model, the secure data processor 128 further determines a set of weight updates. The weight updates may include positive or negative numbers indicating how much a particular weight should be increased or decreased. The weight updates may not include the actual weights. The secure data processor 128 may encrypt the change data (e.g., weight updates and/or corresponding metric updates) with an encryption function H(m) before sending them to the send/receive component 404. The send/receive component 404 may then send the received encrypted weight updates to a weight-filtering component 408 and a metric-filtering component 410, respectively.

The weight-filtering component 408 may filter the weight updates, and the metric-filtering component 410 may filter the metric updates. The filter components 408, 410 may filter the weight and/or metric updates by removing updates greater than a first threshold or lower than a second threshold. The filter components 408, 410 may further normalize the update data by applying a normalization function, such as a sigmoid function.

A weight-summing component 412 may sum the filtered weight updates over several iterations of operation of the gradient descent technique by the secure data processor 128, and metric-summing component 414 may similarly sum the filtered metric updates over several iterations of operation of the gradient descent technique by the secure data processor 128 to create encrypted summation data, which may include the summed encrypted weights and/or summed encrypted metrics. As described herein, the summing components 412, 414 may sum the filtered update data, because the data is additively homomorphic, by multiplying the data together.

Once the available data from the data sources 126 has been applied to the model and once the gradient descent technique has been applied by the secure data processor 128 for all the data, a final weight decode component 416 create decrypted change data by decoding final summed weights, and a final metric decode component 418 may create decrypted change data by decoding final summed metrics using, for example, the decryption function H⁻¹(c) described herein. A success/fail determination component 420 may compare the final metrics to a quality threshold; if the final metrics satisfy the threshold, the system may send the decrypted summation data, which may include the final summed weights, to the model user 124.

With reference to FIG. 4B, the data sources 126 may add noise to their data prior to sending the data, as described herein. In these embodiments, the secure data processor 120 includes additional components to filter and add the data and noise: a weight-noise filter component 430, a weight-and-noise filter component 432, a metric-noise filter component 434, a metric-and-noise filter component 436, weight-noise summing component 438, a weight-and-noise summing component 440, a metric-noise summing component 442, and a metric-and-noise summing component 444. These components may process data in an analogous manner as the weight filter component 408, the metric filter component 410, the weight summing component 412, and the metric summing component 414, respectively, as described above. The final weight decode component 446 may receive the output of both the weight-noise summing component 438 and the weight-and-noise summing component 440 and may remove the noise from the weights, as described above. Similarly, the final metric decode component 448 may receive the output of both the metric-noise summing component 442 and the metric-and-noise summing component 444 and may remove the noise from the metrics. The success/fail determination component 420 may compare the final metrics to a quality threshold; if the final metrics satisfy the threshold, the system may send the final weights to the model user 124.

FIGS. 5A and 5B illustrate a flow diagram for transacting to build a neural network according to embodiments of the present disclosure. Referring first to FIG. 5A, the model user 124 sends, to a market 504, a challenge 508 defining a problem the model user 124 wishes to solve. The market 504 may be, for example, an e-commerce web site that coordinates transfer of data to and from the model provider 122 and the data sources 126. For example, if the model user 124 is a power company, the model user 124 may wish the building of a model to predict failure of a component. The challenge 508 may also include a minimum accuracy of the model in predicting the failure. The challenge 508 may also include a minimum data quality and/or minimum data amount.

The secure data processor 120 and/or model provider 122 sends, to the market 504, an indication 510 to initiate a search for available challenges. The indication 510 may include types of challenges that the secure data processor 120 and/or model provider 122 are capable of solving, compensation requirements, and/or timeframes for solving. The market 508 may send challenge search results 512 back to the secure data processor 120 and/or model provider 122; the search results 512 may include an indication of the challenge 508. Similarly, one or more data sources 126 may send an indication 514 to initiate a search for available challenges. The indication 514 may include the type of data that the data source 126 is offering, the quality of the data, and/or the amount of the data, as well as compensation requirements. The indication 514 may further include a requirement that the data source 126 also be a model user 124. The market 504 may similarly send a result 516 back to the data source 126; the result 516 may include an indication of the challenge 508. If the secure data processor 120 and/or model provider 122 accepts the challenge, it may send an offer to solve 518 back to the market 504; the data source 126 may similarly send an offer 520 to send data. The secure data processor, model provider 122, and or market 504 may determine an estimated amount of computing resources required to solve the problem; this amount may be specified in, for example, the offer to solve 518. The offer to solve 518 may include a payment amount request that is based on the estimated amount of computing resources.

The market 504 may send, to the model user 124, an indication 522 to inspect the accepted offers. The model user 124 may evaluate the offers based on a number of criteria, such as completion time and cost. If the model user 124 accepts one or more offers, it sends a corresponding indication 524 of acceptance to the market 504.

Once the offer is accepted, the model user 124 sends the agreed-upon payment to an escrow service 502. Once the escrow service 502 receives the payment, it sends an indication 528 to start the challenge to a network 506, such as the network 199. The network 506 sends a corresponding indication 530 to start the challenge to the secure data processor 120 and/or model provider 122.

The secure data processor 120 and/or model provider 122 writes code corresponding to the challenge and sends the written code 532 to the network 506, which sends corresponding code 534 to one or more data sources 126. The data sources 126 apply their data to the code and send the results 536 of the running the challenge to the escrow service 502, which sends a corresponding solution 538 to the challenge to the model user. As discussed above, the solution 538 may be a set of weights and/or initial weights and weight updates for the model. The model user 124 may request additional challenges to further improve the model; for example, the model user 124 may send, to the market 504, further requests for data. If the model user 124 accepts the solution 538, the escrow service 502 sends a first payment 540 to the data source 126 and a second payment 542 to the secure data processor 120 and/or model provider 122. In some embodiments, the payments are made using self-executing (i.e., “smart”) contracts.

As mentioned above, a neural network may be trained to perform some or all of the computational tasks described herein. An example neural network 600 is illustrated in FIG. 6. The neural network 600 may include nodes organized as an input layer 602, one or more hidden layers 604, and an output layer 606. The input layer 602 may include m nodes, the hidden layer(s) 604 may include n nodes, and the output layer 606 may include o nodes, where m, n, and o may be any numbers and may represent the same or different numbers of nodes for each layer. Each node of each layer 602, 604, 606 may include computer-executable instructions and/or data usable for receiving one or more input values and for computing an output value. Each node may further include memory for storing the input, output, or intermediate values. One or more data structures, such as a long short-term memory (LSTM) cell or other cells or layers (as described in greater detail with reference to FIG. 8), may additionally be associated with each node for purposes of storing different values. Nodes 602 a, 602 b, . . . 602 m of the input layer 602 may receive inputs 608 a, 608 b, . . . 608 m, and nodes 606 a, 606 b, . . . 606 o of the output layer 206 may produce outputs 610 a, 610 b, . . . 610 o. In some embodiments, the inputs 608 a, 608 b, 608 m correspond to data from a data source, and the outputs 610 a, 610 b, . . . 610 o correspond to model output data. Each node 604 a, 604 b, . . . 604 m of the hidden layer 604 may be connected to one or more nodes 602 a, 602 b, . . . 602 m in the input layer 602 and one or more nodes 606 a, 606 b, . . . 606 o in the output layer 604. Although the neural network 500 illustrated in FIG. 6 includes a single hidden layer 604, other neural networks may include multiple middle layers 604; in these cases, each node in a hidden layer may connect to some or all nodes in neighboring hidden (or input/output) layers. Each connection from one node to another node in a neighboring layer may be associated with a weight or score. A neural network may output one or more outputs, a weighted set of possible outputs, or any combination thereof.

In some embodiments, a neural network is constructed using recurrent connections such that one or more outputs of the hidden layer of the network feeds back into the hidden layer again as a next set of inputs. Such a neural network 700 is illustrated in FIG. 7. Each node of the input layer 702 connects to each node of the hidden layer(s) 704; each node of the hidden layer(s) 704 connects to each node of the output layer 706. As illustrated, one or more outputs 708 of the hidden layer(s) 704 is fed back into the hidden layer 704 for processing of the next set of inputs. A neural network incorporating recurrent connections may be referred to as a recurrent neural network (RNN). An RNN or other such feedback network may allow a network to retain a “memory” of previous states and information that the network has processed.

Processing by a neural network may be determined by the learned weights on each node input and the structure of the network. Given a particular input, the neural network determines the output one layer at a time until the output layer of the entire network is calculated. Connection weights may be initially learned by the neural network during training, where given inputs are associated with known outputs. In a set of training data, a variety of training examples are fed into the network. Each example typically sets the weights of the correct connections from input to output to 1 and gives all connections a weight of 0. As examples in the training data are processed by the neural network, an input may be sent to the network and compared with the associated output to determine how the network performance compares to the target performance. Using a training technique, such as backpropagation, the weights of the neural network may be updated to reduce errors made by the neural network when processing the training data. In some circumstances, the neural network may be trained with an entire lattice to improve speech recognition when the entire lattice is processed.

FIG. 8 illustrates an exemplary long short-term memory (LSTM) cell 800 capable of learning long-term dependencies and which may be used in building one or more of the models described herein. The LSTM cell 800 receives an input vector x_(t) and generates an output vector h_(t). The cell further maintains a cell state C_(t) that is updated given the input x_(t), a previous cell state C_(t-1), and a previous output h_(t-1). Using the previous state and input, a particular cell may take as input not only new data (x_(t)) but may also consider data (C_(t-1) and h_(t-1)) corresponding to the previous cell. The output h_(t) and new cell state C_(t) are created in accordance with a number of neural network operations or “layers,” such as a “forget gate” layer 802, an “input gate” layer 804, a tan h layer 806, and a sigmoid layer 808.

The forget gate layer 802 may be used to remove information from the previous cell state C_(t-1). The forget gate layer 802 receives the input x_(t) and the previous output h_(t-1) and outputs a number between 0 and 1 for each number in the cell state C_(t-1). A number closer to 1 retains more information from the corresponding number in the cell state C_(t-1), while a number closer to 0 retains less information from the corresponding number in the cell state C_(t-1). The output f_(t) of the forget gate layer 402 may be defined by the below equation (17). The layer 802 may be modified by changing one or more of the weights σ, W_(f), and/or b_(f).

f _(t) =σ{W _(f)·[(h _(t-1)),(x _(t))]+b _(f)}  (17)

The input gate layer 804 and the tan h layer 806 may be used to decide what new information should be stored in the cell state C_(t-1). The input gate layer 804 determines which values are to be updated by generating a vector it of numbers between 0 and 1 for information that should not and should be updated, respectively. The tan h layer 806 creates a vector Ċ_(t) of new candidate values that might be added to the cell state C_(t). The vectors it and Ċ_(t), defined below in equations (18) and (19), may thereafter be combined and added to the combination of the previous state C_(t-1) and the output f_(t) of the forget gate layer 402 to create an update to the state C_(t). The layers 804, 806 may be modified by changing one or more of the weights σ, W_(i), b_(i), W_(c), and/or b_(c).

i _(t) =σ{W _(i)·[(h _(t-1)),(x _(t))]+b _(i)}  (18)

Ċ _(t)=tan h{W _(c)·[(h _(t-1)),(x _(t))]+b _(c)}  (19)

Once the new cell state C_(t) is determined, the sigmoid layer 808 may be used to select which parts of the cell state C_(t) should be combined with the input x_(t) to create the output h_(t). The output o_(t) of the sigmoid layer 808 and output h_(t) may thus be defined by the below equations (20) and (21). These values may be further updated by sending them again through the cell 800 and/or through additional instances of the cell 400. The sigmoid layer 808 may be modified by changing one or more of the weights σ, σ_(t), W_(o), and/or b_(o).

o _(t) =σ{W _(o)·[(h _(t-1)),(x _(t))]+b _(o)}  (20)

h _(t) =o _(t)·[tan h(C _(t))]  (21)

The model(s) discussed herein may be trained and operated according to various machine learning techniques. Such techniques may include, for example, neural networks (such as deep neural networks and/or recurrent neural networks), inference engines, trained classifiers, etc. Examples of trained classifiers include Support Vector Machines (SVMs), neural networks, decision trees, AdaBoost (short for “Adaptive Boosting”) combined with decision trees, and random forests. Focusing on SVM as an example, SVM is a supervised learning model with associated learning algorithms that analyze data and recognize patterns in the data, and which are commonly used for classification and regression analysis. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other, making it a non-probabilistic binary linear classifier. More complex SVM models may be built with the training set identifying more than two categories, with the SVM determining which category is most similar to input data. An SVM model may be mapped so that the examples of the separate categories are divided by clear gaps. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gaps they fall on. Classifiers may issue a “score” indicating which category the data most closely matches. The score may provide an indication of how closely the data matches the category.

In order to apply the machine learning techniques, the machine learning processes themselves need to be trained. Training a machine learning component such as, in this case, one of the first or second models, may require establishing a “ground truth” for the training examples. In machine learning, the term “ground truth” refers to the accuracy of a training set's classification for supervised learning techniques. For example, known types for previous queries may be used as ground truth data for the training set used to train the various components/models. Various techniques may be used to train the models including backpropagation, statistical learning, supervised learning, semi-supervised learning, stochastic learning, stochastic gradient descent, or other known techniques. Thus, many different training examples may be used to train the classifier(s)/model(s) discussed herein. Further, as training data is added to, or otherwise changed, new classifiers/models may be trained to update the classifiers/models as desired. The model may be updated by, for example, back-propagating the error data from output nodes back to hidden and input nodes; the method of back-propagation may include gradient descent.

In some embodiments, the trained model is a deep neural network (DNN) that is trained using distributed batch stochastic gradient descent; batches of training data may be distributed to computation nodes where they are fed through the DNN in order to compute a gradient for that batch. The secure data processor 120 may update the DNN by computing a gradient by comparing results predicted using the DNN to training data and back-propagating error data based thereon. In some embodiments, the DNN includes additional forward pass targets that estimate synthetic gradient values and the secure data processor 120 updates the DNN by selecting one or more synthetic gradient values.

FIG. 9 is a block diagram illustrating a computing environment that includes a server 900; the server 900 may be the secure data processor 120, model provider 122, model user 124, and/or data source 126. The server 900 may include one or more input/output device interfaces 902 and controllers/processors 904. The server 900 may further include storage 906 and a memory 908. A bus 910 may allow the input/output device interfaces 902, controllers/processors 904, storage 906, and memory 908 to communicate with each other; the components may instead or in addition be directly connected to each other or be connected via a different bus.

A variety of components may be connected through the input/output device interfaces 902. For example, the input/output device interfaces 902 may be used to connect to the network 199. Further components include keyboards, mice, displays, touchscreens, microphones, speakers, and any other type of user input/output device. The components may further include USB drives, removable hard drives, or any other type of removable storage.

The controllers/processors 904 may processes data and computer-readable instructions, and may include a general-purpose central-processing unit, a specific-purpose processor such as a graphics processor, a digital-signal processor, an application-specific integrated circuit, a microcontroller, or any other type of controller or processor. The memory 908 may include volatile random access memory (RAM), non-volatile read only memory (ROM), non-volatile magnetoresistive (MRAM), and/or other types of memory. The storage 906 may be used for storing data and controller/processor-executable instructions on one or more non-volatile storage types, such as magnetic storage, optical storage, solid-state storage, etc.

Computer instructions for operating the server 900 and its various components may be executed by the controller(s)/processor(s) 904 using the memory 908 as temporary “working” storage at runtime. The computer instructions may be stored in a non-transitory manner in the memory 908, storage 906, and/or an external device(s). Alternatively, some or all of the executable instructions may be embedded in hardware or firmware on the respective device in addition to or instead of software.

FIG. 10 illustrates a number of devices in communication with the secure data processor 120, model provider 122, model user 124, and/or data source 126 using the network 199. The devices may include a smart phone 1002, a laptop computer 1004, a tablet computer 1006, and/or a desktop computer 1008. These devices may be used to remotely access the secure data processor 120, model provider 122, model user 124, and/or data source 126 to perform any of the operations described herein.

The above aspects of the present disclosure are meant to be illustrative. They were chosen to explain the principles and application of the disclosure and are not intended to be exhaustive or to limit the disclosure. Many modifications and variations of the disclosed aspects may be apparent to those of skill in the art. Persons having ordinary skill in the field of computers and speech processing should recognize that components and process steps described herein may be interchangeable with other components or steps, or combinations of components or steps, and still achieve the benefits and advantages of the present disclosure. Moreover, it should be apparent to one skilled in the art that the disclosure may be practiced without some or all of the specific details and steps disclosed herein.

Aspects of the disclosed system may be implemented as a computer method or as an article of manufacture such as a memory device or non-transitory computer readable storage medium. The computer readable storage medium may be readable by a computer and may comprise instructions for causing a computer or other device to perform processes described in the present disclosure. The computer readable storage medium may be implemented by a volatile computer memory, non-volatile computer memory, hard drive, solid-state memory, flash drive, removable disk, and/or other media. In addition, components of one or more of the modules and engines may be implemented as in firmware or hardware, which comprises, among other things, analog and/or digital filters (e.g., filters configured as firmware to a digital signal processor (DSP)).

Conditional language used herein, such as, among others, “can,” “could,” “might,” “may,” “e.g.,” and the like, unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain embodiments include, while other embodiments do not include, certain features, elements and/or steps. Thus, such conditional language is not generally intended to imply that features, elements and/or steps are in any way required for one or more embodiments or that one or more embodiments necessarily include logic for deciding, with or without other input or prompting, whether these features, elements and/or steps are included or are to be performed in any particular embodiment. The terms “comprising,” “including,” “having,” and the like are synonymous and are used inclusively, in an open-ended fashion, and do not exclude additional elements, features, acts, operations, and so forth. Also, the term “or” is used in its inclusive sense (and not in its exclusive sense) so that when used, for example, to connect a list of elements, the term “or” means one, some, or all of the elements in the list.

Disjunctive language such as the phrase “at least one of X, Y, Z,” unless specifically stated otherwise, is otherwise understood with the context as used in general to present that an item, term, etc., may be either X, Y, or Z, or any combination thereof (e.g., X, Y, and/or Z). Thus, such disjunctive language is not generally intended to, and should not, imply that certain embodiments require at least one of X, at least one of Y, or at least one of Z to each be present. As used in this disclosure, the term “a” or “one” may include one or more items unless specifically stated otherwise. Further, the phrase “based on” is intended to mean “based at least in part on” unless specifically stated otherwise. 

What is claimed is:
 1. A computer-implemented method comprising: receiving, from a first data source, first encrypted input data; receiving, from the first data source, first encrypted noise data; receiving, from a second data source, second encrypted input data; receiving, from the second data source, second encrypted noise data; generating encrypted summation data corresponding to a sum of the first encrypted input data and the second encrypted input data; and generating summation data by decrypting, based at least in part on the first encrypted noise data and the second encrypted noise data, the encrypted summation data.
 2. The computer-implemented method of claim 1, wherein generating the encrypted summation data comprises using a multiplication operator on the first encrypted input data and the second encrypted input data.
 3. The computer-implemented method of claim 1, further comprising: receiving, from a device associated with a model provider, a neural-network model; determining, based at least in part on the summation data, an output of the neural-network model; and determining, using a gradient descent algorithm, at least one updated weight of the neural-network model.
 4. The computer-implemented method of claim 3, further comprising: determining a performance metric based at least in part on comparing the output to an expected output; determining that the performance metric satisfies a quality threshold; and based at least in part on determining that the performance metric satisfies the quality threshold, sending, to a device associated with a model user, the at least one updated weight.
 5. The computer-implemented method of claim 4, further comprising: generating a random number, wherein determining the output of the neural-network model is based at least in part on the random number; and based at least in part on determining that the performance metric satisfies the quality threshold, sending, to the device associated with the model user, the random number.
 6. The computer-implemented method of claim 1, further comprising: determining that unencrypted input data corresponds to a fixed-point value; determining a number of decimal places of the fixed-point value; determining a block size corresponding to a size of a portion of the unencrypted input data; sending, to the first data source and the second data source, an indicator of the number of decimal places; and sending, to the first data source and the second data source, an indicator of the block size.
 7. The computer-implemented method of claim 6, further comprising: determining, based at least in part on the block size, a plurality of blocks of data corresponding to the summation data; generating second summation data based at least in part on the plurality of blocks of data; and generating fixed-point summation data based at least in part on the second summation data and the number of decimal places.
 8. The computer-implemented method of claim 1, further comprising: receiving, from the first data source, third encrypted noise data, the third encrypted noise data corresponding to a first random number represented in the first encrypted input data; receiving, from the first data source, fourth encrypted noise data, the fourth encrypted noise data corresponding to a second random number represented in the second encrypted input data; generating second summation data by decrypting, based at least in part on the third encrypted noise data and the fourth encrypted noise data, the summation data.
 9. The computer-implemented method of claim 1, further comprising: generating, by the first data source, a random number; generating, by the first data source, the first encrypted noise data by encrypting the random number; and generating, by the first data source, the first encrypted input data by encrypting a sum of the random number and input data sending, by the first data source, the first encrypted input data and the first encrypted noise data.
 10. The computer-implemented method of claim 1, wherein the first encrypted input data corresponds to a first encryption technique and wherein the first encrypted noise data corresponds to a second encryption technique different from the first encryption technique.
 11. A system comprising: at least one processor; and at least one memory including instructions that, when executed by the at least one processor, cause the system to: receive, from a first data source, first encrypted input data; receive, from the first data source, first encrypted noise data; receive, from a second data source, second encrypted input data; receive, from the second data source, second encrypted noise data; generate encrypted summation data corresponding to a sum of the first encrypted input data and the second encrypted input data; and generate summation data by decrypting, based at least in part on the first encrypted noise data and the second encrypted noise data, the encrypted summation data.
 12. The system of claim 11, wherein the instructions that cause the computing system to generate the encrypted summation data comprise using a multiplication operator on the first encrypted input data and the second encrypted input data.
 13. The system of claim 11, wherein the at least one memory further comprises instructions that, when executed by the at least one processor, further cause the system to: receive, from a device associated with a model provider, a neural-network model; determine, based at least in part on the summation data, an output of the neural-network model; and determine, using a gradient descent algorithm, at least one updated weight of the neural-network model.
 14. The system of claim 13, wherein the at least one memory further comprises instructions that, when executed by the at least one processor, further cause the system to: determine a performance metric based at least in part on comparing the output to an expected output; determine that the performance metric satisfies a quality threshold; and based at least in part on determining that the performance metric satisfies the quality threshold, send, to a device associated with a model user, the at least one updated weight.
 15. The system of claim 14, wherein the at least one memory further comprises instructions that, when executed by the at least one processor, further cause the system to: generate a random number, wherein determining the output of the neural-network model is based at least in part on the random number; and based at least in part on determining that the performance metric satisfies the quality threshold, send, to the device associated with the model user, the random number.
 16. The system of claim 11, wherein the at least one memory further comprises instructions that, when executed by the at least one processor, further cause the system to: determine that unencrypted input data corresponds to a fixed-point value; determine a number of decimal places of the fixed-point value; determine a block size corresponding to a size of a portion of the unencrypted input data; send, to the first data source and the second data source, an indicator of the number of decimal places; and send, to the first data source and the second data source, an indicator of the block size.
 17. The system of claim 16, wherein the at least one memory further comprises instructions that, when executed by the at least one processor, further cause the system to: determine, based at least in part on the block size, a plurality of blocks of data corresponding to the summation data; generate second summation data based at least in part on the plurality of blocks of data; and generate fixed-point summation data based at least in part on the second summation data and the number of decimal places.
 18. The system of claim 11, wherein the at least one memory further comprises instructions that, when executed by the at least one processor, further cause the system to: receive, from the first data source, third encrypted noise data, the third encrypted noise data corresponding to a first random number represented in the first encrypted input data; receive, from the first data source, fourth encrypted noise data, the fourth encrypted noise data corresponding to a second random number represented in the second encrypted input data; generate second summation data by decrypting, based at least in part on the third encrypted noise data and the fourth encrypted noise data, the summation data.
 19. The system of claim 11, wherein the at least one memory further comprises instructions that, when executed by the at least one processor, further cause the system to: generate, by the first data source, a random number; generate, by the first data source, the first encrypted noise data by encrypting the random number; and generate, by the first data source, the first encrypted input data by encrypting a sum of the random number and input data send, by the first data source, the first encrypted input data and the first encrypted noise data.
 20. A computer-implemented method comprising: receiving, from a first data source, first encrypted input data corresponding to a first encryption technique; receiving, from the first data source, first encrypted noise data corresponding to a second encryption technique different from the first encryption technique; receiving, from a second data source, second encrypted input data corresponding to the first encryption technique; receiving, from the second data source, second encrypted noise data corresponding to the second encryption technique; generating encrypted summation data corresponding to a sum of the first encrypted input data and the second encrypted input data; and generating summation data by decrypting, based at least in part on the first encrypted noise data and the second encrypted noise data, the encrypted summation data. 